The oil industry has long been interested in fluid flow properties of porous media. An article by A. Timur entitled "Pulsed Nuclear Magnetic Resonance Studies of Sandstones" in the Journal of Petroleum Technology, June 1969, illustrated that nuclear magnetic resonance measurements could be used to derive fluid flow properties of porous media.
Nuclei with a odd number of protons, like hydrogen nuclei, become aligned parallel to a static magnetic field. These aligned nuclei result in a net magnetic moment parallel to the direction of the static magnetic field, similar to a small dipole magnet aligned with the earth's magnetic field. That condition is the lowest energy state of the system.
An external force, in the form of a radio frequency pulse at the Larmor frequency, can perturb the system to a higher energy state. The result is that the net magnetic moment is reoriented. After removal of the radio frequency pulse, the nuclei return to the lowest energy state through relaxation processes. Relaxation process have been described in a book by T. C. Farrar and E. D. Becker entitled "Pulse and Fourier Transform NMR Introduction to Theory and Methods", 1971 Academic Press, New York, p. 458 and a book by J. C. Davis entitled "Advanced Physical Chemistry", 1965, The Ronald Press Company, New York, p. 577.
Relaxation is governed by molecular dynamics. In liquids, relaxation is controlled by the size and interactions of the molecules. Water and oil have different relaxation characteristics and different crude oils have different relaxation characteristics because of compositional variation. In porous media, saturated with a fluid, relaxation is complex. Molecules near the solid surface can interact with that surface which enhances the relaxation rate. The relaxation rate is proportional to the surface area-to-volume ratio of the pores. The constant of proportionality, termed the surface relaxivity, describes the relaxation provoking power of the surface.
Two time constants are derived from nuclear magnetic resonance measurements. The longitudinal or spin-lattice relaxation time (T.sub.1) refers to a rate constant that characterizes the return of the net magnetization parallel to the static magnetic field. The transverse or spin-spin relaxation time (T.sub.2) refers to a rate constant that characterizes the decay rate of magnetization in an X-Y plane.
Nuclear magnetic resonance measurements can be made with laboratory spectrometers and well logging sondes. These instruments are designed to detect the change in magnetization as a function of time. That data is then used to derive the relaxation rate constants. For any instrument configuration, the apparatus will only respond to nuclei within a defined volume. Different nuclei are sensed because each type of nucleus can only be reoriented by a radio frequency pulse with a certain frequency. For the hydrogen nuclei, that frequency is 42.5759 MHZ/Tesla.
T.sub.2 measurements are the most commonly used NMR measurement in well logging and for petrophysical applications. They are less time consuming than T.sub.1 measurements and can be made with a moving well logging sonde. A paper by W. E. Kenyon et al., entitled "Pore Size Distributions and NMR in Microporous cherty Sandstones" in Transactions SPWLA 30th Annual Logging Symposium, Jun. 11-14, 1989, Paper LL, illustrated how nuclear magnetic resonance data could be transformed into volume-to-surface area distributions of the pores contained within a porous media. A second paper by M. G. Prammer entitled "NMR Pore Size Distributions and Permeability At the Well Site" in Transactions 69th Annual Technical and Exhibition of the Society of Petroleum Engineers, Sep. 25-28, 1994, Paper 28368, illustrated another method for deriving volume-to-surface area distributions from nuclear magnetic resonance data.
These volume-to-surface area distributions approximate the pore size distribution of a porous media. The pore size distribution can be transformed to a capillary pressure curve for the equivalent porous microstructure and used to estimate permeability.